Formats: - HTML - YAML - JSON - 2026-07-18T14:25:00.645946
  • lfunc_lfunctions • Show schema
    {'Lhash': '2509475933868834368360699169790', 'a10': [10.630597564084505, 0.0], 'a2': [-2.126119512816901, 0.0], 'a3': [0.0, 0.0], 'a4': [-3.4796158172192238, 0.0], 'a5': [-5.0, 0.0], 'a6': [0.0, 0.0], 'a7': [30.700042579826682, 0.0], 'a8': [24.407035188631326, 0.0], 'a9': [0.0, 0.0], 'accuracy': 100, 'algebraic': True, 'analytic_conductor': 7.965257850774987, 'analytic_normalization': {'__RealLiteral__': 0, 'data': '1.5', 'prec': 10}, 'bad_lfactors': [[3, [[1.0, 0], [0, 0]]], [5, [[1.0, 0], [5.0, 0]]]], 'bad_primes': [3, 5], 'central_character': '135.1', 'coefficient_field': 'CDF', 'conductor': 135, 'conductor_radical': 15, 'conjugate': '2509475933868834368360699169790', 'degree': 2, 'euler_factors': [[[1.0, 0], [2.126119512816901, 0], [8.0, 0]], [[1.0, 0], [0, 0]], [[1.0, 0], [5.0, 0]], [[1.0, 0], [-30.700042579826682, 0], [343.0, 0]], [[1.0, 0], [50.15479616299753, 0], [1331.0, 0]], [[1.0, 0], [15.959231634438448, 0], [2197.0, 0]], [[1.0, 0], [105.66823031680033, 0], [4913.0, 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'4.36119619187413278627252558782371', '5.18630306595890004521382144446334', '7.29905575078858358403604386712175', '8.182743296263062209903294619836251', '8.764726657610715107773695003814491', '10.34141985996437328778945871911005', '10.91472828531969028664698990236557', '12.09537759040453508715304499436091'], 'prelabel': '2-135-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.822278840011204, 'root_angle': 0.5, 'root_number': '-1', 'self_dual': True, 'sign_arg': {'__RealLiteral__': 0, 'data': '0.5', 'prec': 10}, 'spectral_label': 'c3-0', 'types': ['CMF'], 'z1': {'__RealLiteral__': 0, 'data': '1.97962745682211263790175915637', 'prec': 103}, 'z2': {'__RealLiteral__': 0, 'data': '4.36119619187413278627252558782', 'prec': 103}, 'z3': {'__RealLiteral__': 0, 'data': '5.18630306595890004521382144446', 'prec': 103}}
  • lfunc_search • Show schema
    {'algebraic': True, 'analytic_conductor': 7.965257850774987, 'bad_primes': [3, 5], 'central_character': '1.1', 'conductor': 135, 'conductor_radical': 15, 'degree': 2, 'index': 9, 'instance_types': ['CMF'], 'instance_urls': ['ModularForm/GL2/Q/holomorphic/135/4/a/e/1/2'], 'is_instance_Artin': False, 'is_instance_BMF': False, 'is_instance_CMF': True, 'is_instance_DIR': False, 'is_instance_ECNF': False, 'is_instance_ECQ': False, 'is_instance_G2Q': False, 'is_instance_HMF': False, 'is_instance_MaassGL3': False, 'is_instance_MaassGL4': False, 'is_instance_MaassGSp4': False, 'is_instance_NF': False, 'label': '2-135-1.1-c3-0-9', 'motivic_weight': 3, 'mu_imag': [], 'mu_real': [], 'nu_imag': [{'__RealLiteral__': 0, 'data': '0.0', 'prec': 10}], 'nu_real_doubled': [3], 'order_of_vanishing': 1, 'prelabel': '2-135-1.1-c3-0', 'primitive': True, 'rational': False, 'root_analytic_conductor': 2.822278840011204, 'root_angle': 0.5, 'self_dual': True, 'spectral_label': 'c3-0', 'z1': {'__RealLiteral__': 0, 'data': '1.97962745682211263790175915637', 'prec': 103}}
  • lfunc_instances • Show schema
    {'Lhash': '2509475933868834368360699169790', 'Lhash_array': ['2509475933868834368360699169790'], 'factors': ['2-135-1.1-c3-0-9'], 'label': '2-135-1.1-c3-0-9', 'type': 'CMF', 'url': 'ModularForm/GL2/Q/holomorphic/135/4/a/e/1/2'}